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The X-ray binary SS 433, embedded in the W 50 nebula (or supernova remnant W 50), shows bipolar jets that are ejected with mildly relativistic velocities and which extend toward the east and west out to scales of tens of parsecs. Previous X-ray observations revealed twin lobes along the jet precession axis that contain compact bright knots dominated by synchrotron radiation, which provide evidence of electron acceleration in this system. Particle acceleration in this system is substantiated by the recently detected gamma rays with energies up to at least 25 TeV. To elucidate the origin of the knots and particle acceleration sites in SS 433/W 50 further, we report here on detailed, spatially resolved X-ray spectroscopy of its western lobe with Chandra. We detect synchrotron emission along the jet precession axis, as well as optically thin thermal emission that is more spatially extended. Between the two previously known knots, w1 and w2, we discover another synchrotron knot, which we call w1.5. We find no significant synchrotron emission between SS 433 and the innermost X-ray knot (w1), suggesting that electrons only begin to be accelerated at w1. The X-ray spectra become gradually steeper from w1 to w2, and then rapidly so immediately outside of w2. Through comparison with a model taking into account electron transport and cooling along the jet, this result indicates that the magnetic field in w2 is substantially enhanced, which also explains its brightness. We discuss possible origins of the enhanced magnetic field of w2 as well as scenarios to explain the other two knots.